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Liz Munch - Featurization of Persistence Diagrams Using Template Functions for ML Tasks

Applied Algebraic Topology Network via YouTube

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Overview

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This course focuses on teaching the mathematical framework for featurization of persistence diagrams using "template functions" for machine learning tasks. The course covers topics such as topological data analysis, existing methods for statistics and machine learning, coordinate systems, template function definition, and practical examples using different template function families. The intended audience for this course includes individuals interested in topological data analysis, machine learning, and mathematical approaches to data featurization.

Syllabus

Intro
Shape in data
Topological Data Analysis (TDA)
Persistent homology in one slide
Existing Methods for Stats & ML
Finite vs infinte diagrams
A topologist's view of machine learning
Notation for persistence diagrams
8-matchings and Bottleneck Distance
Persistence diagram space is UGLY
Characterization of relatively compact sets
Up a creek?
Coordinate systems
Birth-Lifetime coordinates
Combining a function and a diagram to get a number
Evaluating points
Template function definition
Template functions
what about in practice?
Example template system 1: Tent functions
Example template system 2. Chebychev polynomials
Random diagrams
Manifold Experiment: Coefficients
Current and future work: Adaptive partitioning

Taught by

Applied Algebraic Topology Network

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